Unified Representation of Molecules and Crystals for Machine Learning

TL;DR

This paper introduces a versatile, invariant tensor representation for molecules and crystals that improves machine learning predictions of energies and forces, enabling efficient simulations across diverse atomistic systems.

Contribution

A new many-body tensor representation that is invariant, unique, differentiable, and applicable to both molecules and crystals, enhancing machine learning accuracy and efficiency.

Findings

Competitive energy and force prediction errors demonstrated.

Effective in modeling molecular dynamics and crystal chemistry.

Successfully applied to phase diagrams of transition-metal systems.

Abstract

Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference calculations. For this, kernel learning approaches crucially require a representation that accommodates arbitrary atomistic systems. We introduce a many-body tensor representation that is invariant to translations, rotations, and nuclear permutations of same elements, unique, differentiable, can represent molecules and crystals, and is fast to compute. Empirical evidence for competitive energy and force prediction errors is presented for changes in molecular structure, crystal chemistry, and molecular dynamics using kernel regression and symmetric gradient-domain machine learning as models. Applicability is demonstrated for phase diagrams of Pt-group/transition-metal binary systems.